Decay Behavior Research Articles

Film Thickness Decay and Wear Behavior of Grease-Lubricated Point Contact under Cyclic Variable Loads

For wind turbine applications, there is a cyclic load-varying process between rolling elements and raceways in pitch bearings. This kind of motion can also lead to radial fretting. However, this is seldom addressed under grease-lubricated conditions in the literature. In this study, grease-lubricated point contact problems have been investigated experimentally under cyclic load-varying conditions. The findings revealed that as the load-varying range diminishes, the variation in grease film distribution becomes more subtle and the rate of discharge of thickener fiber clusters in the stick zone decelerates. This is due to the fact that the rate of change in the Hertz contact radius is reduced and the migration of grease is weakened during the unloading process. Due to the large apparent viscosity of grease with a high soap content, entrapped grease is not easily discharged during loading, and the thickness of the film in the stick zone progressively increases as the soap content of the grease is augmented. This also causes the variable load zone to wear out more easily. As the grease is subjected to repeated loading and unloading, there is a gradual reduction in film thickness, and larger thickener fiber clusters tear, resulting in a flattened form and shear thinning. Grease containing sulphur–phosphorus additives demonstrates a superior effect on reducing fretting wear within the large variable load range but generally proves effective for smaller load-varying ranges. This study may offer insights into the degradation of grease under variable load motion and methods to prevent radial fretting wear.

Decay behavior and internal interactions of regularly reflected spherical blast waves

Blast wave reflection is a critical area in military and infrastructure defense, converging shock dynamics, and colliding blast waves. While irregular blast reflections have garnered remarkable attention, research on regularly reflected (RR) blast waves remains comparatively limited. This study presents a detailed literature on shortcomings of post-reflection quantities of RR blast waves and aims to bridge this gap by extensively analyzing RR behaviors of spherical blast waves against a planar surface in air via numerical methods. With 31 scenarios involving a 1 kg charge and scaled distances from 0.5 to 4.0 m/kg1/3, comprehensive field data on parameters including pressure, density, and velocity were gathered using a fan-like gauge array. A dedicated program for tracking the RR shock front was developed, enabling precise trajectory detection and detailed quantitative analyses of RR wave decay. First, accurate empirical trajectory equations for RR waves were formulated along its normal axis. Second, spatial decay analysis was conducted, revealing consistent decay rates for each RR field parameter under 1 m/kg1/3 and diminishing decay rates beyond this threshold. Third, parameter profiles preceding RR shock fronts at various post-reflection distances were examined, while discrepancies and complexities against generalized profiles were uncovered. Qualitatively, this study identified four internal interactions within the reflection phenomenon, categorized by scaled distance ranges, and elucidated the secondary wave's impact on RR wave propagation. The comprehensive quantitative and qualitative findings in this work offer profound insights into blast wave dynamics, addressing several gaps on RR blast wave behaviors and laying a foundation for understanding more complex blast reflection phenomena crucial in various domains.

Investigation of some optical, conducting and radiation shielding properties of Dy3+ ions doped boro-silicate glass systems

Three borosilicate glass samples of 25 % Si2O – 30 % Na2O – 45 % B2O3 doped with x Dy2O3 (where x = 0, 2, and 4 mol %) were prepared using the melt quenching technique. Photoluminescence spectra for glass samples were studied when excited by 350 nm in the 400–800 nm range, where emission sharply increases for samples doped with 2 % Dy2O3 (BSNDy2) at 580 nm after exposed to 30 kGy. Also, glass containing 2 % Dy photoluminescence constants, such as decay curves CIE chromaticity, was measured for all samples that gave three decay behaviors: slow, intermediate, and fast. Experimental lifetime (τexp.), color coordination (X, Y), and yellow/blue intensity ratio (y/b) beside the color correlated temperature (CCT) were determined before and after being irradiated by 30 and 60 kGy from γ ray source where the y/b ratio of BSNDy2 increase by increasing exposure to gamma doses and were >1. In addition, electrical conductivity at different temperatures was investigated as the BSNDy2 sample gave the highest conductivity and decreased by BSNDy4. Moreover, shielding parameters such as the tenth value layer, half value layer, mean free path and mass attenuation coefficient values were calculated at different gamma-ray energies via the Phy-X program, showing the highest values for MAC, Zeff, Neff, and Ceff for BSNDy4 sample. The findings showed that adding Dy2O3 to the glass gave a fortified shielding character.

Analytical and numerical analyses of a viscous strain gradient problem involving type Ⅱ thermoelasticity

<abstract><p>In this paper, a thermoelastic problem involving a viscous strain gradient beam is considered from the analytical and numerical points of view. The so-called type Ⅱ thermal law is used to model the heat conduction and two possible dissipation mechanisms are introduced in the mechanical part, which is considered for the first time within strain gradient theory. An existence and uniqueness result is proved by using semigroup arguments, and the exponential energy decay is obtained. The lack of differentiability for the semigroup of contractions is also shown. Then, fully discrete approximations are introduced by using the finite element method and the backward time scheme, for which a discrete stability property and a priori error estimates are proved. The linear convergence is derived under suitable additional regularity conditions. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximations and the behavior of the discrete energy decay.</p></abstract>

Statistics of detonation confinement: 1D, 2D and 3D simulations in hydrogen–oxygen

Statistical analysis of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) detonation simulations is performed to understand the role of confinement on detonation frontal velocity and thermodynamic states. Simulations considered include a 2D wide channel (5 detonation cells across), a 2D narrow channel (1.5 cells across), a 3D square channel (10 cells around perimeter), and a 3D round tube (6 cells around perimeter), with identical mixture conditions of stoichiometric hydrogen–oxygen with 3000 parts per million by volume (PPMv) ozone at 300 K and 15 kPa. 1D and 2D simulations with the same mixture without ozone are also considered. All simulations solve the compressible Navier–Stokes equations with detailed chemistry and exhibit good agreement with macroscopic characteristics of experiments (e.g., cell size). Results show that the frontal velocity in 3D simulations is more irregular as compared to the 2D simulations, which are more irregular compared to the 1D simulations. The irregularity in frontal velocity leads to broader distributions of shock velocities and shock decay behavior. The 3D simulations also exhibit a wider and more extreme set of thermodynamic states as compared to the 2D simulations immediately behind the shock wave, within the induction zone, and throughout the rest of the domain. Increasing relative boundary losses leads to quantitative differences in both thermodynamic state and frontal velocity, consistent with 1D steady models of detonation with losses. The conclusions drawn in this work are not sensitive to numerical grid resolution.

Temperature and pressure dependent luminescence mechanism of a zinc blende structured ZnS:Mn nanophosphor under UV excitation

Presenting a novel insight into Mn2+ luminescence processes in the ZnS nanophosphor and revealing its unique high-pressure luminescence decay behaviour and self-powered mechanoluminescence.

TESS ve yer-tabanlı gözlemler ışığında WASP-12b'nin güncellenmiş yörünge küçülme oranı

We investigate the orbital decay behavior of the well-studied hot Jupiter WASP-12\,b orbiting its late-F host star on a 1.09-day orbit by analyzing its transit timings. Thanks to precise photometric data covering nearly 15 years of observations from the space and the ground since the discovery of the planet, including a transit light curve of our own, it became possible to study this behaviour in its details. This work updates the orbital period to a new value of 
 $P = 1.0914202527 \pm 0.000000039\,\text{days}$ and agrees with the previous finding that the planetary orbit has been shrinking with an updated rate of $-31.03 \pm 0.94\,\text{ms yr}^{-1}$. This corresponds to an orbital decay timescale of $\tau =P/|\dot{P}| = 3.04 \pm 0.09\,\text{Myr}$ that we attribute to the strong tidal interactions between the host-star and the planet. We also update the reduced stellar tidal quality factor as $Q_{*}^{\prime} = (1.72 \pm 0.39) \times$ $10^{5}$, which corresponds to the lower bound of the previously reported values of the parameter.

Elucidating solvent effects on the stability of phenoxyl radicals in monohydric alcohols via electron paramagnetic resonance

Research on solvent effects is an important and long-standing topic, but there still is some room, especially for the special solvent effect of fluoroalcohols. In this work, we investigated the stability of phenoxyl radical in monohydric alcohol solvents through in-situ electron paramagnetic resonance detections. The decay behavior of phenoxyl radical showed a reasonable relationship with the mesoscopic structure of alcohols, characterized by small- and wide-angle X-ray scattering. Moreover, the distinct solvent effects of fluoroalcohols were emphasized, and the significant influence of van der Waals distance in the solvents was suggested. Overall, the stability of phenoxyl radical in alcohols was quantified and correlated with the solvent structures. We believe that the established method for stability study on radicals will encourage solvent effect studies on various organic reactions, and the proposed solvent effects in fluoroalcohols may inspire the development of green solvents in both industrial conversions and organic synthesis.

Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations

AbstractThe long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models are isotropic Oseen equations where the viscosity acts uniformly in all directions and anisotropic Oseen-type equations with different viscosity directions. The hypocoercivity index is determined (if it exists) and it is shown that similar to the finite dimensional case of ordinary differential equations and differential-algebraic equations it characterizes its decay behavior.

Electroluminescence and temperature-dependent time-resolved photoluminescence of monolithically integrated triple-wavelength InGaN-based LED

Here, we propose a monolithically integrated triple-wavelength InGaN-based LED structure and conduct comprehensive research on its emission dynamics under electrical and optical excitation. Through experimental and numerical analyses, a carrier transport and a recombination process can be manipulated in bandgap-engineered multiple quantum wells (MQWs), thus realizing the manipulation of emission properties. A rational triple-wavelength LED structure is heteroepitaxially grown, which shows excellent color stability versus injected currents. Furthermore, utilizing the temperature-dependent time-resolved photoluminescence (TRPL), triple-wavelength peaks display different TRPL decay behaviors. Especially, an anomalous three-stage decay phenomenon is found for a low-energy peak measured at 10 K, accompanied by a decay profile transition with the increasing temperature. The underlying mechanisms are revealed and correlated with carrier localization, interaction between different QWs, and competition between radiative and nonradiative recombination.

Analyzing asymmetry in the Wolf-Villain model via the study of the persistence of various initial height fluctuations

The Wolf-Villain (WV) model, which, in some literature, has shown trait of up-down asymmetry, is investigated through the study of the persistence probability of height fluctuations in simulated film surfaces. The persistence probability is the probability that the height fluctuation of each site does not cross its initial value (h 0) along a time interval. When averaged over all possible values of h 0, the probability is known to exhibit a power law decay behavior with the exponent called persistence exponent. In this work, instead of averaging over all h 0, we consider a fixed value of h 0 and find that the persistence probability of the WV model still decreases with time as a power law if the fixed value meets a necessary condition, i.e. h 0 is roughly equal to or larger than the saturated roughness of the film. The persistence exponent for each h 0 is measured and found to decrease as the value of h 0 increases. Scaling form of the persistence probability at a specific h 0 is also studied. Notably, all results obtained here are in agreement with those of the up-down symmetric models appeared in literatures despite the fact that the WV model is an asymmetric model. These results support the idea from other studies that the asymmetry in the WV is very weak.

Tunable Light Response Modulated by the Organic Interface Charge Transfer Effect

AbstractThe combination of a donor (D) and an acceptor (A) is viewed as a promising approach to achieve high performance phototransistors, owing to their advantages in exciton dissociation and charge trapping. The electronic properties at the D‐A interface can vary substantially with the choice of materials, and how to precisely control the interface properties to achieve a controllable light response behavior is still an open question. Herein, a series of D‐A heterostructure is reported with varying electronic structures of the acceptor and demonstrate the ability to tune the performance and photocurrent decay behaviors. Two distinct types of charge transfer phenomena, ground state, and excited state charge transfer, are identified originating from the specific different energy level alignment and lead to the improved photoresponsivity up to 104 AW−1 and the significantly varied photosensitivity ranging from 102 to approaching 107. Furthermore, the distinct charge transfer scenarios elicit diverse temporal responses, encompassing both short‐term synaptic behavior as well as persistent memory characteristics. These findings shed light on the importance of understanding and controlling charge transfer property for phototransistor performance and applications. The ability to modulate the temporal responses opens up new possibilities for designing devices with desired memory and synaptic functionalities.

Temperature dependence of growth-sector-dependent Raman spectra of boron-doped diamonds synthesized at high-pressure high-temperature

Single crystals of boron-doped diamond (BDD) were synthesized by the temperature gradient method in high-pressure and high-temperature conditions in the Fe–Al–B–C system, and multisectoral diamond plates were extracted. Temperature-dependent (77–600 K) high-resolution Raman spectroscopic studies have been carried out to investigate the behavior of anharmonic phonon decay in the {001}, {113}, and {111} growth sectors of multisectoral diamond plates with different content of boron impurities (⩽80 ppm) and compare with the data for undoped IIa diamond. Micro-Fourier transform infrared spectroscopy was used to estimate the spatial distribution of uncompensated boron impurity [Na-Nd] in BDD plates by analyzing boron-related absorption peaks. The plates were shown to have non-uniform growth-sector-dependent content of uncompensated boron impurity in the range from 1.1 × 1018 to 1.4 × 1019 cm−3. The effects of anharmonic decay (damping) of optical phonons in BDD are studied by modeling the temperature dependence of phonon frequency and linewidth of the diamond’s F2g and boron-induced vibrational modes. The extrapolated zero-temperature optical phonon linewidth and frequency and the anharmonic nature of their linear relationship are determined as a function of the growth sector and boron doping. The predominant mechanisms and parameters of the anharmonic decay of optical phonons are determined, which is of fundamental importance for the thermal conductivity of semiconductor materials. The anharmonic phonon decay remained the predominant process at higher temperatures, irrespective of the doping level.

Laser Ablation of Silicon Nanoparticles and Their Use in Charge-Coupled Devices for UV Light Sensing via Wavelength-Shifting Properties.

This study explores the controlled laser ablation and corresponding properties of silicon nanoparticles (Si NP) with potential applications in ultraviolet (UV) light sensing. The size distribution of Si NPs was manipulated by adjusting the laser scanning speed during laser ablation of a silicon target in a styrene solution. Characterization techniques, including transmission electron microscopy, Raman spectroscopy, and photoluminescence analysis, were employed to investigate the Si NP structural and photophysical properties. Si NP produced at a laser scanning speed of 3000 mm/s exhibited an average diameter of ~4 nm, polydispersity index of 0.811, and a hypsochromic shift in the Raman spectrum peak position. Under photoexcitation at 365 nm, these Si NPs emitted apparent white light, demonstrating their potential for optoelectronic applications. Photoluminescence analysis revealed biexponential decay behavior, suggesting multiple radiative recombination pathways within the nanoscale structure. Furthermore, a thin film containing Si NP was utilized as a passive filter for a 2nd generation CCD detector, expanding the functionality of the non-UV-sensitive detectors in optics, spectrometry, and sensor technologies.

Universal to nonuniversal transition of the statistics of rare events during the spread of random walks.

Through numerous experiments that analyzed rare event statistics in heterogeneous media, it was discovered that in many cases the probability density function for particle position, P(X,t), exhibits a slower decay rate than the Gaussian function. Typically, the decay behavior is exponential, referred to as Laplace tails. However, many systems exhibit an even slower decay rate, such as power-law, log-normal, or stretched exponential. In this study, we utilize the continuous-time random walk method to investigate the rare events in particle hopping dynamics and find that the properties of the hop size distribution induce a critical transition between the Laplace universality of rare events and a more specific, slower decay of P(X,t). Specifically, when the hop size distribution decays slower than exponential, such as e^{-|x|^{β}} (β>1), the Laplace universality no longer applies, and the decay is specific, influenced by a few large events, rather than by the accumulation of many smaller events that give rise to Laplace tails.

ANALISIS FUNGSI KORELASI KLASIK DAN KUANTUM UNTUK MODEL CINCIN: SEBUAH REVIEW

A review of the journal entitled 'Classical And Quantum Correlation Functions For A Ring Model' has been carried out which discusses the solutions of classical and quantum correlation functions for the ring model. Classical and quantum correlation functions are derived for systems of non-interacting particles moving in a circle. demonstrated that the decay behavior of the classical expression for the correlation function can be recovered from a strictly periodic quantum mechanical expression by taking the limit ℏ→0, after the appropriate transformation. The aim of this study is to present clearly and in detail how the position correlation function for a system of particles moving in a circle having a certain average energy and written in a form which shows the nature of the transformation. Next, we examine the use of Poisson addition to represent F(z), and how the correlation function becomes identical to the form given by classical statistical mechanics, which exhibits Gaussian decay. The results of this study indicate that the positional correlation function for a system of particles moving in a circle, and having a certain average energy, can be written in a form which shows the nature of the transformation. Then using the Poisson addition formula to represent F(z), the expression is rewritten to enable the limit ℏ→0 to be taken. It was finally found that the correlation function became identical to the form given by classical statistical mechanics, which exhibits a Gaussian decay.

Development of Highest Value of the Measured Efficiency of Mesoporous Petal Shaped Europium (III) Doped Cobalt Tetroxide@Cupric Oxide Hybrid Nanomaterials for Enhanced Room Temperature Photoluminescence and Fluorescence Decay Properties.

In our work, a novel series of europium (III) (Eu3+) (5, 10 and 15 wt %) doped cobalt tetroxide@cupric oxide (Co3O4@CuO) nanomaterials (NMs) were synthesized by facile coprecipitation method. The synthesized NMs were characterized by XRD (X-ray diffraction), FT-IR (Fourier transform infrared), UV (ultraviolet)-visible absorption spectra, XPS (X-ray photoelectron), BET (Brunauer-Emmett-Teller) analytical methods. Crystal structure studies revealed the formation of polycrystalline nature with monoclinic and cubic phase. The morphology studies of Eu3+x:Co3O4@CuO (x = 5, 10 and 15 wt %) showed petal shape nanoparticles (NPs) with agglomeration. Redshift in optical absorption spectra appeared with a significant impact on the optical band gap as Eu3+ concentration increases on Co3O4@CuO bimetallic oxide NMs. The chemical composition and valence state of the elements confirmed from XPS studies detected the presence of Eu, Cu, Co, O and C elements. An increase in the pore size and surface area resulted as the Eu3+ concentration increased on Co3O4@CuO NMs. However, room temperature photoluminescence (RTPL) spectra of Co3O4@CuO bimetallic oxide NMs at two different excitations (λ excitation = 280nm, 320nm) showed sharp, strong emission intensities located at near ultraviolet (NUV) region and weak emissions detected at far ultraviolet (FUV) regions of the RTPL spectrum. Further, visible range emission intensities were displayed by Eu3+:Co3O4@CuO (5, 10 and 15 wt %) NMs when exited at 280nm. The characteristic white light emission peaks in the visible range of the RTPL spectra showed intense blue, green and orange colours. Emission intensity increases with an increase in Eu3+ concentration on Co3O4@CuO bimetallic oxide NMs. The fluorescence (FL) decay spectra of Eu3+ 10wt% and 15 wt%: Co3O4@CuO NMs showed a decay lifetime of 2.54 and 2.31ns (ns) attributed to the dynamic, ultrafast excitation energy transfer between Eu3+ (dopant) and Co3O4@CuO (host) NMs. It is proposed that enhanced RTPL emission intensity and FL decay behavior of Eu3+x:Co3O4@CuO NMs closely related to the change in the optical band gap, variation in the crystallite size, formation of more number of oxygen vacancies in the crystal structure of hybrid nanomaterials.

Off-diagonal approach to the exact solution of quantum integrable systems

We investigate the t–W scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of the transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated operator (see Eqs. () and ()) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation (the t–W relation without the W-term) can be used to study the ground state properties of quantum integrable systems with/without U(1)-symmetry in the thermodynamic limit.

Efficient CrIII Ion Governed Energy Migration for Broadband Near‐Infrared Emission in Ca3Sc2Ge3O12 Garnet Phosphor

AbstractThe rapid growth in phosphor‐converted near‐infrared light‐emission diodes (NIR‐LEDs) has led to the development of NIR emitter with high efficiency, broadband emission and high thermal stability. In this work, an efficient broad NIR emission of Cr3+ in novel Ca3Sc2Ge3O12 (CSGO) garnet‐based host was developed for the first time, which located at 700 to 1000 nm peaking at 817 nm with a broad bandwidth of ~128 nm. Such a broadband NIR emission originated from the preferential occupancy of Cr3+ in Sc3+ sites with weak octahedral field, which was manifested by the luminescence spectrum and decay behaviors. The Cr3+‐doping concentration was regulated to achieve a good internal quantum efficiency (IQE) of 72.1 % and a fantastic thermal stability (at 423 K, sustained approximately 85 % of the initial intensity). The mechanism for concentration and thermal quenching was further investigated. Benefiting from the excellent luminescence features, a prototype NIR‐LEDs was assembled via integrating the optimized samples with commercial blue InGaN LED chips, which exhibited a satisfactory photoelectric property and a brilliant performance in night vision. These results demonstrated the as‐obtained sample to be a great potential candidate for NIR‐LEDs.

Analysis of the strong vertices of ΣcΔD∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}\\Delta D^{*}$$\\end{document} and ΣbΔB∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{b}\\Delta B^{*}$$\\end{document} in QCD sum rules

In this work, we analyze the strong vertices ΣcΔD∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{c}\\Delta D^{*}$$\\end{document} and ΣbΔB∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Sigma _{b}\\Delta B^{*}$$\\end{document} using the three-point QCD sum rules under the tensor structures iϵρταβpαpβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i\\epsilon ^{\\rho \ au \\alpha \\beta }p_{\\alpha }p_{\\beta }$$\\end{document}, pρp′τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{\\rho }p'^{\ au }$$\\end{document} and pρpτ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p^{\\rho }p^{\ au }$$\\end{document}. We firstly calculate the momentum dependent strong coupling constants g(Q2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g(Q^{2})$$\\end{document} by considering contributions of the perturbative part and the condensate terms ⟨q¯q⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle {\\overline{q}}q\\rangle $$\\end{document}, ⟨gs2GG⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle g_{s}^{2}GG \\rangle $$\\end{document}, ⟨q¯gsσGq⟩\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle {\\overline{q}}g_{s}\\sigma Gq\\rangle $$\\end{document} and ⟨q¯q⟩2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle {\\overline{q}}q\\rangle ^{2}$$\\end{document}. By fitting these coupling constants into analytical functions and extrapolating them into time-like regions, we then obtain the on-shell values of strong coupling constants for these vertices. The results are g1ΣcΔD∗=5.13-0.49+0.39GeV-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{1\\Sigma _{c}\\Delta D^{*}}=5.13^{+0.39}_{-0.49}\\,\\hbox {GeV}^{-1}$$\\end{document}, g2ΣcΔD∗=-3.03-0.35+0.27GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{2\\Sigma _{c}\\Delta D^{*}}=-3.03^{+0.27}_{-0.35}\\,\\hbox {GeV}^{-2}$$\\end{document}, g3ΣcΔD∗=17.64-1.95+1.51GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{3\\Sigma _{c}\\Delta D^{*}}=17.64^{+1.51}_{-1.95}\\,\\hbox {GeV}^{-2}$$\\end{document}, g1ΣbΔB∗=20.97-2.39+2.15GeV-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{1\\Sigma _{b}\\Delta B^{*}}=20.97^{+2.15}_{-2.39}\\,\\hbox {GeV}^{-1}$$\\end{document}, g2ΣbΔB∗=-11.42-1.28+1.17GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{2\\Sigma _{b}\\Delta B^{*}}=-11.42^{+1.17}_{-1.28}\\,\\hbox {GeV}^{-2}$$\\end{document} and g3ΣbΔB∗=24.87-2.82+2.57GeV-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{3\\Sigma _{b}\\Delta B^{*}}=24.87^{+2.57}_{-2.82}\\,\\hbox {GeV}^{-2}$$\\end{document}. These strong coupling constants are important parameters which can help us to understand the strong decay behaviors of hadrons.